Resources
Numerical accuracy
The calculations in our apps: the policy each one is under, the precision it runs at, and the code itself.
This device: processor, memory, graphics The standard Precision is not robustness
Calculation policies
A policy says how one family of calculations keeps its precision. Open one to see its calculations, by source file, and their code.
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Heating and cooling loads per room
Works out what bounds each room, the U-value of each bounding element, and from them the design heating load, a degree-day year and a cooling peak.
- BimCraft
- 11 calculations
64-bit -
Hollowing a body to a wall thickness
Makes the inside surface that leaves a wall of the asked thickness, reports the volume taken out, and builds drain holes through the wall.
- ModelCraft
- 8 calculations
32-bit in part Open item -
Hours of direct sun on the ground and on walls
Counts the hours of direct sun each ground cell and each wall point of the building masses gets on chosen days, with the masses and the terrain casting shadows.
- CivilCraft
- 9 calculations
32-bit in part Open item -
Hull hydrostatics and righting arms
Works out a floating part's displaced volume, displacement, centers of buoyancy and flotation, metacentric heights and the righting-arm curve at a given draft.
- PartCraft
- 5 calculations
32-bit in part Open item -
Hull lines: fairness measures and fairing
Measures how fair a hull curve is (inflections, curvature jumps, roughness) and rebuilds it with fewer control points within a tolerance.
- PartCraft
- 5 calculations
64-bit -
Hull surfaces to a closed solid and its volume
Joins NURBS patches into one closed triangle mesh, mirrors and caps it, and works out its volume.
- PartCraft
- 5 calculations
64-bit -
I/O channel counts with spare allowance
Counts the control system channels of each type on a P&ID and adds the spare allowance.
- CadCraft
- BimCraft
- 1 calculation
64-bit Open item -
IFC 4.3 infrastructure quantities and files
Reads the quantities, stations and alignment lengths of roads, railways, bridges and other infrastructure from an IFC file, totals them per class, and writes a new IFC 4.3 file.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 9 calculations
64-bit Open item -
IFC alignment curves and stations
Reads the alignment curves of an IFC 4.3 file as sampled 3D polylines, finds the point at a station, places elements along them and builds solids swept between cross sections.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 7 calculations
64-bit Open item -
IFC curves and profiles as point lists
Turns the curves and cross-section profiles of an IFC file into polylines: arcs, circles, ellipses, trimmed curves, B-splines, offsets, and the standard steel shapes with their fillets.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 10 calculations in 2 files
64-bit Open item -
IFC export
Writes the steel parts, holes, copes, mitre cuts, bolts, footings, bars and grids of the model as an IFC4 file.
- DetailCraft
- 10 calculations
64-bit Open item -
IFC export of parts, assemblies and library items
Writes the mesh, placements, quantities and parameter values of a part, an assembly or a library item into an IFC4 file.
- PartCraft
- 6 calculations
32-bit in part Open item -
IFC export: geometry and quantities gathered from the project
Turns the project's alignments, corridors, pads, walls, track, pipes and parcels into the meshes, lengths, areas and volumes that the IFC export writes.
- CivilCraft
- 15 calculations
64-bit Open item -
IFC export: numbers written to the file
Writes the whole project as an IFC file: coordinates, alignment parameters, lengths, areas, volumes and unit factors as text.
- CivilCraft
- 25 calculations
64-bit Open item -
IFC faces on curved surfaces
Tessellates faces that lie on cylinders, cones, spheres, tori, swept surfaces and B-spline surfaces into triangles.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 11 calculations
64-bit -
IFC geometry handed to the apps
Gives each app an element's triangles and the matrix that places them, in meters with Y up, moved near the origin.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 4 calculations
32-bit in part Open item -
IFC import
Turns the steel members, plates, holes, copes, bolts, grids and levels of an IFC file into a DetailCraft model.
- DetailCraft
- 14 calculations
64-bit Open item -
IFC import: alignments, surfaces and units
Reads alignments, terrain surfaces and reference geometry from an IFC file into project coordinates and units.
- CivilCraft
- 13 calculations
64-bit -
IFC length unit and placement matrices
Finds how many millimeters one length unit of an IFC file is, and multiplies, inverts and applies the 4 × 4 placement matrices used when reading and placing elements.
- BimCraft
- 6 calculations
64-bit -
IFC measures in SI for USD
Converts IFC lengths, areas and volumes to meters, square meters and cubic meters when properties are written to USD.
- CadCraft
- BimCraft
- ModelCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- PartCraft
- 1 calculation
64-bit -
IFC openings, clippings and half-space cuts
Cuts openings and clipping solids out of an IFC element's mesh, so the element is drawn and measured with its voids.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 8 calculations
32-bit in part Open item -
IFC swept solids, primitives and faceted shapes
Builds the meshes of extruded, revolved and swept solids, swept disks such as rebar and pipes, the basic primitives, and faceted boundary shapes.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 10 calculations in 2 files
64-bit -
IFC units and placements
Reads the length and angle units of an IFC file and turns its placements, transformation operators, grid placements and map conversion into 4 × 4 matrices.
- BimCraft
- TakeoffCraft
- CivilCraft
- DetailCraft
- 13 calculations in 2 files
64-bit -
IGES files of NURBS curves and surfaces
Writes B-spline curves and surfaces to an IGES file in millimeters and reads them back, converting the file's unit.
- ModelCraft
- PartCraft
- 5 calculations
64-bit Open item -
Illuminance values written on the lighting plot
Places the fixtures of a plot in millimeters for the photometric engine and writes the computed lux at each grid point as text in the drawing.
- CadCraft
- 2 calculations
64-bit -
Illustrate: projection, hidden lines and vector pictures
Projects a manual view onto the picture, removes hidden lines and writes the result as line art and PDF pages.
- PartCraft
- 4 calculations in 4 files
32-bit, display only -
Illustrate: vector, matrix and rigid-fit math
Places points with 4 × 4 matrices, inverts them, and finds the rigid move that best maps one set of points onto another.
- PartCraft
- 8 calculations
64-bit -
Import of a parametric export file
Rebuilds a part feature by feature from a cadcraft-sw-export file: sketches moved into the part's planes, edges and faces found from their positions, parameters and equations carried over, and the volume compared with the one in the file.
- PartCraft
- 11 calculations
32-bit in part Open item -
Import of DXF and DWG drawings into the 3D model
The edges and faces made when a DXF or DWG drawing is brought into the 3D model as a site plan: unit scaling, block placement, and arcs, circles, ellipses and splines turned into straight segments.
- CadCraft
- ModelCraft
- 15 calculations
64-bit Open item -
Import of OBJ, glTF and Collada models
The vertex positions and placements read from an OBJ, glTF or Collada file, turned to the model's Z-up meters.
- CadCraft
- ModelCraft
- 8 calculations
64-bit -
Imported carbon factors, prices and climate data
Reads a person's own carbon-factor file, cost book or climate answer into the tables the carbon, cost and solar panes calculate from.
- BimCraft
- 5 calculations
64-bit Open item -
Imported material parameters
Turns a glTF or FBX material's numbers (roughness, index of refraction, film thickness, emission strength) into the renderer's parameters and back.
- ModelCraft
- 4 calculations
64-bit Open item -
Inset, bevel and moves along normals
Places the new vertices of an inset or a bevel at the stated thickness or width from the old edges, and moves vertices along their normals.
- ModelCraft
- 7 calculations
64-bit -
Installation loads and cable lengths
Adds up the load on each electrical circuit of a building plan, works out its current, and measures each circuit's cable along the drawn routes.
- CadCraft
- 10 calculations
64-bit -
Interference between assembly parts
Finds pairs of placed parts that overlap, with the overlapping volume, and steps a joint through a range to check for clashes along the way.
- PartCraft
- 3 calculations
32-bit in part Open item -
Interior elevations and their dimensions
Frames each wall of a room as an interior elevation, writes its width, height and level dimensions, and turns placed items.
- BimCraft
- 7 calculations in 2 files
64-bit -
Inverse kinematics and constraints
Moves a bone or a placement so it reaches a target, looks at it, copies it, stays within limits, hangs from it or sits on a path.
- ModelCraft
- 11 calculations in 2 files
64-bit -
Inverse kinematics and joint trajectories
Joint angles that put a robot link at a target, and timed joint moves with their speeds, accelerations and peak torques.
Every app 64-bit, stated limit- 9 calculations in 2 files
64-bit -
Irrigation zones: flow, pressure and coverage
Adds up the flow of each irrigation zone, works out the pressure it needs at the valve and at the supply, the precipitation rate and run time, and checks head coverage.
- CivilCraft
- 20 calculations in 2 files
64-bit Open item -
Issue viewpoints in BCF files
Converts cameras and section planes between the viewer and the model's own coordinates, and writes and reads them in BCF issue files.
- BimCraft
- ModelCraft
- 8 calculations
64-bit Open item -
Join and stretch
Joins lines, arcs and polylines that line up or meet end to end into one object, and stretches the parts of objects inside a window.
- CadCraft
- 3 calculations
64-bit -
Joist depth from a span table the person loads
Picks the smallest joist depth whose listed clear span reaches the span asked for, from a table the person loads.
- BimCraft
- 6 calculations
64-bit -
Keys dragged in the graph editor
Turns a drag on the curve editor's canvas into a key's new time and value, or a handle's new offset.
- ModelCraft
- 3 calculations
64-bit -
KISS file: quantities, sizes and weights
Writes the bill of materials as a KISS file for fabrication software: quantities, sizes, lengths, weights and plate areas.
- DetailCraft
- 6 calculations
64-bit Open item -
Knot vectors
Builds and checks the knot vectors that NURBS curves and surfaces are defined on.
- ModelCraft
- PartCraft
- 6 calculations
64-bit -
Lab results to stream composition
Turns lab results in mass, mole, ppm or mg/L terms into a proposed stream composition in mole fractions, and writes calculated compositions back in the lab's terms.
- CadCraft
- BimCraft
- 2 calculations
64-bit -
Landscape grading: platforms, swales, slope classes and ponding
Shapes the proposed ground from platforms, berms, swales and free grading areas, and reads the surface for slope classes and ponds.
- CivilCraft
- 6 calculations
64-bit Open item -
Landscape IFC export
Writes plants, beds, hedges, planted areas, hardscape and freeform objects to an IFC file in meters.
- CivilCraft
- 7 calculations
64-bit Open item -
Landscape sections and detail drawings
Cuts a section line through the ground, walls, paving, planted areas, steps and plants and lays the result out to scale on a sheet, and draws wall, paving and step details from their numbers.
- CivilCraft
- 11 calculations in 3 files
64-bit -
LandXML export and import
Writes points, surfaces, alignments, profiles, pipe networks and feature lines as LandXML, and reads them back.
- CivilCraft
- 16 calculations
64-bit Open item
A policy is added only after its source was read. Each statement can be checked in the code shown on its page; the app repositories are public. When a release changes a calculation, its page says so until it has been read again.
The standard
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64-bit everywhere
Every calculation runs in 64-bit floating point (IEEE 754 double precision), from the number you type to the number you read.
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15 digits, always
A 64-bit number keeps any 15-digit value intact and takes 17 digits to write out in full. Our rule for every calculation: carry all 17 between steps, and order the arithmetic so that avoidable rounding never costs one of the first 15.
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32-bit gets a warning
A 32-bit number keeps about 7 digits. Where a 32-bit step can reach a number you read, the calculation is flagged in the lists below, and the app will warn that the result can have less mathematical precision.
This device
What this browser can see of your machine. It is shown here only and sent nowhere; the desktop app reads the full hardware, a web page cannot.
The apps calculate in 64-bit on every device. Work handed to the graphics processor is the exception: browsers expose graphics processors as 32-bit calculators, which can provide less mathematical precision.
- Processor
- Memory
- Numbers in the apps
- Graphics processor (WebGL)
- WebGPU
A browser reports a rounded or capped view of the machine, never a full inventory: it gives the number of processor threads (not the model), memory rounded down and capped at 8 GB (Chromium only), and one graphics adapter even when a machine has several. What the browser reports about graphics is a capability, not a measurement of the card. The size of a graphics card's memory bus (a 192-bit bus, for example) says how fast data moves, not how precisely it calculates. Most graphics cards can calculate in 64-bit natively, slowly, but WebGL and WebGPU do not offer it to web pages.
Approaches
Every policy takes one of five approaches to keeping its precision.
- Exact values 8 policies
- Constants and factors are held as exact fractions from their definitions. The arithmetic is ordered so that no rounded factor is ever used.
- Exact predicates 1 policy
- Coordinates are 64-bit. The yes-or-no decisions that shape the geometry (which side of a line, inside or outside a circle) are computed exactly, so rounding cannot flip one.
- 64-bit, direct 337 policies
- Every value is a 64-bit number from input to result. Formulas are closed form or a direct solve, and every comparison uses a stated tolerance.
- 64-bit, stated limit 428 policies
- The arithmetic is 64-bit, but the method or the data sets the accuracy: a solver tolerance, a mesh, a step size, a datum shift, a table. The limit is stated where the result is shown.
- Display only 49 policies
- Computed to draw the screen, often in 32-bit on the graphics processor. No number a person reads, saves or exports comes from it.
- 32-bit step, flagged 118 policies
- One step stores or exchanges 32-bit values that reach a number a person reads. It is listed here with its open item, and the step is either moved to 64-bit or the app will warn where the number is read.
Precision is not robustness
Mathematical precision is how many digits a number keeps. Geometric robustness is whether a shape stays valid: every intersection found, every solid closed, every face joined to its neighbors. They are different properties, and a CAD system can have the first without the second.
Every geometric algorithm rests on yes-or-no questions. Is this point left or right of that line? Do these two edges cross? Is this point inside that circle? Each answer is the sign of a small expression. When three points are almost in line, the true value of that expression can be smaller than the rounding error of the arithmetic that computes it, and the sign comes out wrong. That happens at 15 digits as readily as at 7.
One wrong sign is not a small error in the last digit. It is a different decision: an intersection that is missed, two triangles that overlap, a face that points the wrong way, a solid with a gap in it. Every coordinate can be correct to 15 digits while the shape they describe is invalid.
What makes geometry robust
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Exact predicates
The yes-or-no questions are answered exactly. The fast 64-bit answer is used when it is safely away from zero. When it is not, the sign is computed again with as many digits as it takes.
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Decide once
A decision about a shape is recorded as topology, and every later step agrees with it. The same question is never asked twice with a chance of two answers.
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Stated tolerances
Where a tolerance is used it is written down, scaled to the size of the geometry and applied the same way everywhere.
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Local origins
Coordinates far from zero are moved to a local origin before the work, so the digits are spent on the geometry and not on the distance to the origin.
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Valid by construction
Algorithms whose result is guaranteed to be a closed solid, whatever the input, in place of ones that repair the result afterwards.
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More than the language
These choices matter more than the programming language. JavaScript, C++ and Rust all compute with the same 64-bit numbers: the same algorithm is as robust, or as fragile, in each.
Where our apps stand
The list on this page records both properties. Surface triangulation in CivilCraft and BimCraft uses exact predicates. Solid modeling in PartCraft runs on a kernel whose result is a closed solid by construction. The intersections in the CadCraft app use stated tolerances today, and exact tests for the near-parallel and near-tangent cases are an open item. Each policy says which approach it takes.